Piscotty departed in the fifth inning with a head contusion, and the team says he will be evaluated again on Wednesday.
Piscotty reached when he was hit by a pitch from Jake Arrieta. He was hit again by catcher Willson Contreras' throw when he stole second.
Piscotty then scored from second on Kolten Wong's infield hit to the right side of the mound. Cubs second baseman Javier Baez threw home, but the ball went off Piscotty's head.
"I've never seen (a trip around the bases) like that before," Cardinals manager Mike Matheny said.
OUCH: Cardinals outfielder Steven Piscotty suffered a head injury after being hit 3 times in just one inning! pic.twitter.com/WL0fd8BbG5— ABC World News Now (@abcWNN) April 5, 2017
Piscotty, who agreed to a $33.5 million, six-year contract a day earlier, was down on the field for several minutes after being hit Tuesday night. He eventually walked off the field.
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